For example, in the experiment shown in Figure 4a,b, we set σ= λ/ C and compared the performance at different values of C. We then use an efficient sparse computation to produce the following three sums at each CpG site x i in (x1,…, x n ): The second and third of these sums, S K (i) and S KK (i), depend only on the CpG sites, { x i }, not the statistics, { Y i }.
The second term (E x (λ i )) depends only on the relative power spectrum of the illuminant and the third term (S x (λ i )) depends only on the reflectance of the object's surface.
Suppose that the validation probability π i = P(ξ i = 1|X i,A i ) depends only on (Z i,A i ).
With regards to primal ergodic variables r notice that each Lagrangian maximizing rate r i depends only on λ i and that we can compute each r i =r i (λ i ) separately as r i ( λ i ) = arg max r i ∈ r min, r max U ( r i ) − λ i r i. (70).
From the definition of left edges, we know that the probability p({ s}, S, K i) depends only on the edges in L(K i).
Consequently, J ς (x ) = ∑ i = 1 M J Ω L L (x − c i ), depends only on the function J Ω L (r ) and the deviations x − c i, where c i is the closest lattice point of c i + L to x.
In TANTAN, however, the emission at position i depends only on the residue at position i - k in such a way that the two symbols k positions apart are equal with high probability.
(3 Because of the thinning property of Poisson distribution, conditional on R, Y i follows a Poisson distribution: Moreover, because each Y i depends only on the corresponding X i and, conditional on R, the X i's are independent of each other, the Y i's are independent Poisson random variables.
The data are said to be MAR, given the covariates x i if, for all i, R i is independent of the missing entries of Y i, given those that are observed and x i. Equivalently, the MAR assumption can be expressed as the requirement that the density of R i |(Y i x i ) depends only on Y i through the entries that are observed.
The square root of the angular velocity of fluid, ω12f — calculated from Id — depends only on the ω12r — value irrespective of the concentration and the physical properties of the fluid.
From (B2), we see that the values D i,; k, depend only on S i +1,; k +1,.
